From my experience, I think you can speed up by choosing which clues you deal with first, rather than simply going through the list.

I choose to complete the clues in the following order:
1. The 5 people are - this always gives you 9 X's on your grid, so dealing with this first makes that clear.
2. The Positive clues - eg Polly drinks cola
3. The Negative clues - eg Polly does not drink cola
4. The remaining clues

You will find that once you get used to the process, you will get much faster. That process is the same one I use, and it works well for me. The other thing I do that helps me get faster time is that after I do the 5 people clue, I do all the clues that have the ranking in them (either $ amt, times, place in line, etc.). Then all the other positive clues, negative clues, and then the remaining clues.

I'm slow and methodical, so I x most negatives, until I get to the point that I'm moving known positives from the bottom to the top. If I have all the positives in second and third squares down the left, I don't finish second down on the right. You'll know after a while when you have enough info to have all the answers and it's safe to skip some x's.
If you have access to more than one computer, try them all, it makes a big difference. Some just react faster and smoother. Screen shape changes it. With some screens, not all clues fit on the screen and you have to scroll down. Personally, I do better if I take my time because then I don't make mistakes and have to start over.
Interuptions and distractions are my biggest problem.